No, and I didn't frame it that way either. I'm troubled by part of your answer which identify the property owner as the automatic aggressor (and the initiator of force):
It isn't self defense if you are in hot pursuit, you have become the aggressor. Your right to use deadly force ceases when your life (or family and friends) is no longer in danger[...]If you go out and become the aggressor (taking the gun from someone) and shoot them, you didn't act in self defense.
Except the thief is physically contending for physical possession of the owner's deadly weapon. Doesn't that dispute endanger the owner as well?
It seems to me you are implying the owner has a burden to release the weapon into the hands of any thief who grabs it. Shouldn't the thief have the same burden to release the weapon into the hands of the owner without a dispute? We are very clear on who is the thief and who is the owner, after all. As well we are clear on who is carrying the deadly weapon - the thief, not the owner. The rustling analogy does not apply, because the owner is not executing a thief who is already arrested.
Suppose the owner with a deadly weapon in hand attempts to arrest the thief. The thief then disputes the arrest with a deadly weapon. Who is responsible for initiating violence? Who is acting in self defense when they use deadly force?
This discussion is offending the libertarian in me. I don't recall the part where eschewing the initiation of force means open season for thievery and no recourse never...
Sorry but when you go after someone to get your property back you become the aggressor. That may not be right, but that is the way it is.
Except the thief is physically contending for physical possession of the owner's deadly weapon. Doesn't that dispute endanger the owner as well?
Sure, but this was initiated by the owner, that is aggression on his part. The thief can plead self defense here.
It seems to me you are implying the owner has a burden to release the weapon into the hands of any thief who grabs it.
No if the gun is in your possession and a thief tries to grab it you are completely justified in killing and shooting the thief. Once the thief has the gun and is running away (the running away part is very important) you are not justified in racing after the thief and grabbing the gun and shooting the thief.
Suppose the owner with a deadly weapon in hand attempts to arrest the thief. The thief then disputes the arrest with a deadly weapon. Who is responsible for initiating violence? Who is acting in self defense when they use deadly force?
Citizen arrests are tricky. Depending on the circumstances the owner is probably justified in killing the thief if it takes place at the scene of the crime. But and this is a huge but, it is very likely that the owner will be charged with murder if the citizen arrest takes place away from the crime scene. You can't go and hunt the thief down.
This discussion is offending the libertarian in me. I don't recall the part where eschewing the initiation of force means open season for thievery and no recourse never...
No recourse? We are talking about the use of deadly force. There is no problem with calling the cops, tackling the guy and beating him to a pulp (may get you in some trouble, but it is doubtful). The bottom line though is that you can't use deadly force merely to protect property.
Do you really think that if someone comes on your property and steals something that you can shoot them?